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3
votes
1answer
120 views

Conservative FV Immersed boundary method for compressible flow

Is there a conservative FV second-order (or first-order) accurate immersed boundary method for compressible flow including moving boundaries (in the literature)? By compressible flow I mean the ...
0
votes
1answer
72 views

Finding maximum value in huge dataset

I am working on a project involving some pattern recognition. For this I need to find the maximum value in a huge multidimensional dataset. For example I have a discrete 5-dimensional space containing ...
1
vote
1answer
153 views

Implicit finite difference scheme for LWR-v PDE

I want to discretize the LWR(Lighthill-Whitham-Richards)-v partial differential equation (as shown in 1) $$ \frac{\partial u}{\partial t} + \frac{\partial R(u)}{\partial x} = 0 \quad \text{i.e.,} \...
1
vote
1answer
56 views

an over view of sparsity promoting inversion techniques [closed]

I have a function called f(x) which is convex and I can have access to its first order derivative , my objective function is $$\ J(\bf{x}) = f(\bf{x}) + \lambda |\bf{x}|_0 $$ $$\ \bigtriangledown ...
9
votes
5answers
1k views

Is discontinuous Galerkin really any more parallelizable than continuous Galerkin?

I've always heard that easy parallelization was one of the advantages of DG methods, but I don't really see why any of those reasons don't also apply to continuous Galerkin.
2
votes
1answer
64 views

last column of SPD matrix given it's spectral decomposition

I'm working on this application where I get the spectral decomposition (O,D) of a matrix A for free (A is of full rank) but not A itself, and I need to only recover the last column of A. I was ...
1
vote
1answer
106 views

gather data from processors in FFTW3 MPI

The parallel FFTW3 distributes different portions of a large data to different processors, so that each processor obtains and manipulates only a small fraction of the large size data that wants to be ...
10
votes
1answer
713 views

What is the impact of C++11 move semantics in the context of scientific computing?

C++11 introduces move semantics which can, for example, improve code performance in situations where C++03 would need to perform a copy construction or copy assignment. This article reports that ...
14
votes
2answers
1k views

Why would a computational scientist need to implement their own version of std::complex?

Many of the better-known C++ libraries in computational science such as Eigen, Trilinos, and deal.II use the standard C++ template header library object, ...
2
votes
0answers
108 views

Modal analysis of structure with aerodynamic damping

I'm using modal decomposition to predict the steady state response of a beam structure to harmonic loading. The structure itself is very lightly damped, but we know from experiments that the ...
0
votes
1answer
808 views

Matlab: Error in integral function

I want to compute an integral with the following code written in Matlab. ...
10
votes
4answers
4k views

Linear programming with matrix constraints

I have an optimization problem that looks like the following $$ \begin{array}{rl} \min_{J,B} & \sum_{ij} |J_{ij}|\\ \textrm{s.t.} & MJ + BY =X \end{array} $$ Here, my variables are matrices $...
3
votes
1answer
868 views

Von Neumann stability analysis in 3d

I need to get a stability criterion for the numerical scheme for equation $$\frac{\partial u}{\partial t}-\frac{\partial^2 u}{\partial x^2}-\frac{\partial^2 u}{\partial y^2}-\frac{\partial^2 u}{\...
2
votes
2answers
91 views

Neural Networks: what's the point of learning features that don't linearly separate?

Unless I'm mistaken, deep neural networks are good for learning functions that are nonlinear in the input. In such cases, the input set is linearly inseparable, so the optimisation problem that ...
0
votes
1answer
255 views

Harwell-Boeing format for sparse matrices

I'm dealing with SVDLIBC library. In order to compute singular values I need to specify my matrix in the Harwell-Boeing format. On Internet I have found next example: Dense Text Format: ...
1
vote
1answer
112 views

Optimization for differential and nonlinear system [closed]

I want to minimize a cost function for a differential-nonlinear system (dynamic). Is it possible to use this software? How can I do it? Best regards, Haniye
5
votes
3answers
2k views

Monte Carlo estimation of Pi with Buffon's needle

Is there a way of estimating Pi with the Buffon's method without assuming Pi known? To be more precise: in a Monte Carlo simulation of the experiment invented by Buffon I would (ideally) generate 2 ...
1
vote
0answers
295 views

Rank one constraint in optimization, which is nonconvex, but will we find the global maximum?

The objective function is $L = D(B)$, here $D$ is a function of $B$ and $D$ is a convex function. We have a prior information of $B$: it is rank one and we can write $B$ into $B = pq^T$. So we can ...
4
votes
3answers
4k views

Conservation of Mass in 1D Advection-Diffusion Equation

My long-term goal is to numerically solve the 1D advection-diffusion equation of the form: $$\frac{\partial u}{\partial t}=\frac{\partial }{\partial x}\left( v(x,t) u+D\frac{\partial u}{\partial x}\...
2
votes
1answer
285 views

Monte Carlo normalization of a wave function

I would like to normalize a quantum mechanical multi-particle wave function numerically, and since the result is a multidimensional integral I thought Monte Carlo methods might be appropriate. So, I'm ...
2
votes
1answer
463 views

2d pseudo-spectral turbulence simulation with random initial velocities

I am trying to write a 2d pseudo-spectral DNS code with random initial velocities. This is kind of a classic simulation where the very tiny vortices group together forming larger and larger vortices ...
0
votes
1answer
407 views

Custom CVX Functions - Overriding Errors [closed]

I have constructed a function in Matlab that is convex and increasing (qualitatively similar to an exponential function but I am hoping to avoid the successive approximation requirement of exp). In my ...
4
votes
3answers
7k views

Can numpy.linalg.solve use back substitution when possible?

The question is if Python Numpy library can use back subsitution to solve Ax=b if possible, that is, if A is lower triangular? Do numerical linear algebra packages do this? I would think Numpy would ...
3
votes
0answers
2k views

BFGS Fails to Converge

The model I'm working on is a multinomial logit choice model. It's a very specific dataset so other existing MNLogit libraries don't fit with my data. So basically, it's a very complex function ...
3
votes
1answer
1k views

Courant Friedrichs Lewy condition - how to get it?

I am interested, how can we get CFL condition for every type of PDE? It's known that for 1st order linear equation $$\frac{\partial u}{\partial t}+a\frac{\partial u}{\partial x}=0 $$ CFL is get from ...
2
votes
3answers
2k views

How to solve (continuous) quadratic programming problem with non-PSD matrix

In which problem category can I put a quadratic programming problem with only continuous values whereas the matrix A should be symmetric but needs not to be positive semi-definite? ...
1
vote
1answer
156 views

large symmetric positive band matrix

I use gpbsv command from Intel MKL to solve symmetric positive band system. But unfortunately when the system is large I get an error Access violating writing location in VisualStudio. Could someone ...
7
votes
2answers
722 views

Evaluation of Vandermonde matrix

I would like to construct a Finite Element basis by using a generalized Vandermonde matrix. The idea is to compute the values of a suitable modal basis ('prime basis') at a set of points in reference ...
2
votes
1answer
3k views

Modelling rotating machinery other than AMI rotating meshes

I have case of a rotating fan at Low- speed ie about 300-400 rpm. I have successfully carried out RAS simulations using cyclicAMI approach where, the motion of the fan is modeled as rigid body ...
0
votes
2answers
2k views

What to do with singular (non-invertible) rotation matrix

I have an orthotropic material with a (6x1) stress vector known in the global coordinate system and yield surfaces known in a local coordinate system. So far I have only needed to convert from local ...
4
votes
1answer
349 views

Meshes in codes that do AMR

In light of this question and some stuff I read online I am wondering if large FE libs (e.g., deal.ii, libmesh etc.) that do AMR keep the entire mesh or possibly a coarse version of the entire mesh on ...
6
votes
2answers
489 views

Minimizing 1D convex functions

I have a one dimensional convex function $$f : [a,b] \to \mathbb{R}$$ and want to find the minimum value $$\min_{a \le x \le b} f(x)$$ I know all derivatives of $f$, so the problem could easily be ...
10
votes
2answers
560 views

Which novel data structures are used in adaptive FEM?

A lot of adaptive FEM libraries use more advanced mesh data structures to handle adding/removing nodes, edges, triangles, tetrahedra, etc. For example, the p4est library uses octree data structures ...
13
votes
4answers
1k views

Estimating hardware error probability

Say I run a supercomputer computation on 100k cores for 4 hours on http://www.nersc.gov/users/computational-systems/edison/configuration, exchanging about 4 PB of data over the network and performing ...
1
vote
1answer
51 views

detecting special $2 \times 2$ matrices in a large array of zeros and ones

I have a large array of zeros and ones and I need to count instances of 0 1 1 0 0 0 1 1 0 1, 1 0, 1 1, 0 0 And I would like to exclude all ...
3
votes
0answers
119 views

Spatio-temopral wavelet analysis

Am quite new to wavelet analysis and would like some help. I am performing a spatio-temporal analysis of monthly gridded rainfall data. With PCA, I can reduce the dimension of the rainfall data into a ...
4
votes
0answers
101 views

Tracking for two meshes

I'm dealing with physical simulation (position based dynamic). Now I'm trying to realize tracking for two meshes. In order to explain what does it mean, let's assume that we have two similar meshes: ...
7
votes
3answers
2k views

Finite-size effects in molecular dynamics simulation

I will be blunt: this is an old exam question of a course that covers Molecular Dynamics (MD) and Monte Carlo (MC) simulations. Explain how to determine the severity of finite-size effects. My ...
3
votes
0answers
40 views

Solving ODE boundary problem with additional conditions

I need to solve two point bondary problem for ODE. The solution of the problem itself is very easy. The real issue is that when solving arising non linear system of equations it always converges to ...
4
votes
4answers
2k views

Library that performs sparse matrix-vector and matrix-transpose-vector multiplication

My main interest is sparse matrix-vector and matrix-transpose-vector multiplication of the form y=y+AA'x. Is there any library that performs ...
1
vote
1answer
645 views

Line segment straddle

What is exactly the definition of "Straddle"? Can you please explain what do they mean exactly or a sketch? A segment P1P2 Straddles a line if point P1 lies on the one side of the line and point P2 ...
3
votes
2answers
625 views

In what regime do the continuous and discontinuous Galerkin method become unstable for advection-diffusion systems?

I know that the finite volume method (based around a central different stencil) is unstable for advection dominated advection-diffusion problems. This leads to different adaptive schemes to can be ...
1
vote
0answers
195 views

Shift-Invert in Anasazi/Belos using Tpetra Sparse Matrices

I am currently trying to port my code over to Trilinos because the problems that I am working on are too big for LAPACK/ARPACK. Specifically I am computing the generalized eigenvalues/eigenvectors: $$...
2
votes
2answers
2k views

visualization of 3D probability flow

I have a master equation for $P(N_A^+,N_B^+,N_C^+,t)$, with $N_A^+,N_B^+,N_C^+$ all discrete. The numerical integration is done by this Matlab program using Euler's method. Despite the crude Euler's ...
6
votes
2answers
360 views

Is there any numerical reason for not using repeated multiplication instead of integer powers?

I recently discovered that, in MATLAB 2013b at least, it is significantly faster to do repeated multiplication rather than integer powers. That is, ...
9
votes
1answer
448 views

Is there some good mailing list for `Computational Science`?

I am wondering whether there is some very good mailing list or google groups for Computational Science, where we can discuss questions instead of only asking and replying questions. In fact, I am ...
0
votes
0answers
135 views

Algorithms to compute largest gap between smallest nonzero eigenvalues of sparse symmetric matrix

I am looking mainly for c/c++ implementations but also for theoretical algorithms to compute gaps between smallest positive eigenvalues of symmetric, singular matrix or real numbers. To be precise, I ...
3
votes
3answers
154 views

Can anyone recommend a pipeline dependency ("make") tool for SGE jobs?

I am looking for a tool to specify pipelines of arbitrary multiple jobs with dependencies for the Sun Grid Engine. I can wire things together myself but I am hoping for something more declarative and ...
3
votes
0answers
94 views

Numerical Quadrature of Oscillating Integral With Non-oscillating part

As you will know there are different numerical integrals (I believe Levin's method is the most popular one) for the numerical quadrature of oscillating integrands which may roughly speaking be written ...
1
vote
1answer
373 views

Convex objective function of matrix with prescribed determinant and trace

I have real symmetric positive definite matrix $M = \left(\begin{matrix} a & b \\ b & c \end{matrix}\right)$ where $a,b,c \in R,\ a,c>0,\ \left|b\right|<2\sqrt{a c}$. I want to define ...

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